EPISODE · Feb 1, 2012 · 52 MIN
Juggler's Exclusion Process
from Hamilton Institute Seminars (HD / large) · host Hamilton Institute
Speaker: Prof. L. Leskelä Abstract: Juggler's exclusion process describes a system of particles on the positive integers where particles drift down to zero at unit speed. After a particle hits zero, it jumps into a randomly chosen unoccupied site. I will model the system as a set-valued Markov process and show that the process is ergodic if the family of jump height distributions is uniformly integrable. In a special case where the particles perform jumps according to an entropy-maximizing fashion, the process reaches its equilibrium in finite nonrandom time, and the equilibrium distribution can be represented as a Gibbs measure conforming to a linear gravitational potential. Time permitting, I will also discuss a recent result which sharply characterizes uniform integrability using the theory of stochastic orders, and allows to interpret the dominating function in Lebesgue's dominated convergence theorem in a natural probabilistic way. This talk is based on joint work with Harri Varpanen (Aalto University, Finland) and Matti Vihola (University of Jyväskylä, Finland).
What this episode covers
Speaker: Prof. L. Leskelä Abstract: Juggler's exclusion process describes a system of particles on the positive integers where particles drift down to zero at unit speed. After a particle hits zero, it jumps into a randomly chosen unoccupied site. I will model the system as a set-valued Markov process and show that the process is ergodic if the family of jump height distributions is uniformly integrable. In a special case where the particles perform jumps according to an entropy-maximizing fashion, the process reaches its equilibrium in finite nonrandom time, and the equilibrium distribution can be represented as a Gibbs measure conforming to a linear gravitational potential. Time permitting, I will also discuss a recent result which sharply characterizes uniform integrability using the theory of stochastic orders, and allows to interpret the dominating function in Lebesgue's dominated convergence theorem in a natural probabilistic way. This talk is based on joint work with Harri Varpanen (Aalto University, Finland) and Matti Vihola (University of Jyväskylä, Finland).
NOW PLAYING
Juggler's Exclusion Process
No transcript for this episode yet
Similar Episodes
May 31, 2026 ·25m
May 31, 2026 ·30m
May 31, 2026 ·57m
May 31, 2026 ·32m
May 31, 2026 ·29m
May 31, 2026 ·37m